1. Suppose we have a uniform magnetic field, B, directed into the plane of the diagram below, whose magnitude varies sinusoidally as indicated. Immersed in this magnetic field is the
d) Now let's put in some "typical" numbers: Suppose: r = 1 cm.
R = 1000 ohms.
f = 60 Hz. (typical power line frequency)
e) Since the (varying) induced magnetic field would also produce an induced emf, can we ignore this effect in the calculation for induced emf that we used in part a)?
f) Answer question e) if the frequency were 6 MHz (6 ?106 Hz), a typical radio frequency.
2 In the circuit shown below, the switch is thrown to position a, charging the capacitor to voltage V. When the switch is thrown to position b, the circuit becomes an ideal oscillator consisting of a capacitor, C, and an inductor, L, and will oscillate forever.
FYI: This is a frequency right in the middle of the visible light range. Since most solids do absorb and reflect visible light preferentially, and since it can be assumed that the light interacts with the electrons, could it be that a model of a solid with electrons "tethered" in place with a spring constant of about 10 N/m could "explain" the colors of objects?
In other words, incoming light "shakes" the electrons, and if you "shake" a charge, it emits light at the frequency of the "shaking". At and near the resonant frequency of the "tethered" electrons, the shaking would be greatest, and so would the frequency of the light emitted. Thus, the resonant frequency could determine the "color" we see.
3. An ambulance travels down a highway at a speed of 120 km/h. Its siren emits sound at a frequency of 800 Hz. What is the frequency heard by a passenger in a car traveling at 90 km/h, in the opposite direction (a) as the car approaches the ambulance and (b) as the car moves away from the ambulance? Take the speed of sound as 340 m/s.
4. The index of refraction of glass is different for different wavelengths. Flint glass has an index of refraction of 1.478 for blue light ( ? = 430 nm) and 1.402 for red light ( ? = 680 nm). A beam of light, consisting of these two colors, is directed into a rectangular flint glass block, at
an incidence angle of 50? to the normal. The block is 10 cm thick.
(a) Find the angle between the two color beams as they pass throygh the glass
(b) Find the distance between the beams at the instant they leave the glass.
(c) Do the emerging beams converge, diverge, or stay parallel?
5. A converging lens, of focal length 18 cm, is to form an image of an 8.0 cm high object.
(a) Find the position, size and nature of the image, if the object distance is: 10 cm.
(b) Show the image formation in this case by means of a ray diagram.
(c) Find the position, size and nature of the image, if the object distance is: 30 cm.
(d) Show the image formation in this case by means of a ray diagram.
6. (a) The fundamental frequency of a pipe closed at one end is 512 Hertz, and the speed of sound is 344 m/s. How long is the pipe?
(b) Two whistles having frequencies of 408 Hz and 414 Hz are sounded simultaneously. How many beats are heard per minute?
(c) What is the wavelength in meters of waves broadcast by a TV station whose frequency is 65 MHz?
7. A loudspeaker and a sound reflecting wall are arranged so that the listener hears sound both directly from the speaker, and reflected from the wall. See diagram below. If the distance d, between the source and listener, is 10.0 m, and the sound is a pure sinusoid with a frequency of 68.0 Hz, what is the smallest distance, h, greater than zero, such that destructive
interference cancels the sound at the listener's position? (Take the speed of sound to be 340 m/s.) Take into account that the reflected wave from the wall has a one-half wavelength phase difference on reflection (this is analogous to the wave on a string reflecting from a rigid post).
8. Light is incident normally upon the long face of a symmetric prism, as shown in the figure below, but the angle ? is adjustable (may not be 90?). Angles ? and ? are equal, and the angles of a triangle must add up to 180?. What is the range of values of angle ? that will permit total reflection form both the rear faces for glass with an index of refraction 1.55?
9. A clothesline has a linear mass density of 0.28 kg/m, and is stretched with a tension T = 30 N. One end is given a sinusoidal motion with a frequency of 5.0 Hz and amplitude of 0.010 m. At the time t = 0 the end has zero displacement and is moving in the positive y-direction.
(a) Find the wave speed, the amplitude, the frequency, period, wavelength, and the wave number, of the wave motion.
(b) Write a wave function describing the wave.
(c) Find the position of the point at x = 0.25 m at time t = 0.10 sec.
10. A string is fastened between two posts such that the tension is held at a constant value. Each of the posts is mounted in a tube that allows it to slide up and down without affecting
the tension. At T = 0, the left-hand post is briefly raised upward, then returned to its starting position. At the same time, the right-hand post is briefly lowered, then returned to its starting position. At T = 1 second, the result of this, is a pair of pulses that are traveling in opposite directions, and have opposite amplitudes, as shown below.
